Your best bet is to look at Hopfield networks. They are auto-associative artificial neural networks (ANNs) which model some aspects of human memory. That is, the behavior of Hopfield networks under certain learning rules is similar to the performance of certain human memory (the kind that would end up in the frontal cortex as opposed to, say, the cerebellum).
Like human memory, Hopfield networks do not exhibit "perfect" recall for all input vectors. However, the recall will be strongest when the input is closest to the recall vector. Sometimes, a Hopfield network will converge to the "opposite" of the intended recall vector (something which doesn't seem to happen to humans, possibly because of additional filtering circuitry rejecting such recalls...or perhaps, this does happen, but manifests itself in subtle ways).
The size of the vector stored in a Hopfield net is equal to the number of nodes in the network. That is, the nodes themselves represent both the inputs to the memory and the manifested outputs. This may or may not be similar to the way parts of the human brain are organized. If it is indeed similar, then we can derive a few bits of performance data.
The number of "storable" vectors in a Hopfield network appears to be about 14%. So let's say you have a network which stores the names of people and places you know. In order to reliably store 1000 names, you would need about 7000 neurons. Pretty good, huh? Now imagine you need to store their faces. Uh-oh. The human retina has more than 3 million photoreceptors, which is about 1 million pixels, accounting for color. If you tried to store images at full resolution, then, you would need a network of 3 million neurons. Then you could store about 400k distinct images (assuming the vectors are sufficiently different). However, it is very likely that visual memories are not stored in the brain in this way, due to the fact that the higher brain only has access to the output of the visual cortex, which does a tremendous amount of pre-processing (edge and segment detection along multiple angles, movement detection, etc.).
So how many neurons do we have to work with? The raw total for humans is about 86b. But much of the brain is control circuitry (for operating your automatic functions like heart rate, digestion, etc., skeletal muscles, other organs). If we limit ourselves to the cerebral cortex, which is where "higher order memories" are most likely to be stored, we are looking at about 21b neurons, or about a quarter of the total.
At this point, it could be tempting to work backwards, and say that the human brain could then store about 3 billion memories. But remember that a Hopfield network stores vectors which are the length of the number of nodes in the network, so these "memories" would be ~3 GB each!!! And we know by the wiring of the cerebral cortex that it cannot possibly be a single Hopfield network. A Hopfield network is also fully connected (every node connects to every other), and the cortex is highly layered. On average, human neurons connect to about 7000 neighbors. Thus, if the brain contains any Hopfield networks at all, they are likely to be fairly small.
In the limiting case where the entire cortex is composed of Hopfield nets (not plausible), we would have ~3 million networks which can each store about 1000 vectors of ~1 KB each. Although that is still 3 billion total vectors, we now have the challenge of mapping these vectors onto memories. We must thus ask: "What is a memory?" The fact that Americans celebrate Thanksgiving day in November might be considered a memory. And the fact that they tend to travel to be with family might also be considered a memory. But what about last Thanksgiving? Is the smell of turkey a memory? How about the smell of turkey + sweet potatoes + apple pie? Are those distinct memories or pieces of the same memory? Is the football game part of the "last Thanksgiving" memory, or its own memory?
The fact that memories are inherently fuzzy does't help matters any. They do not have crisp boundaries, and they can be hierarchical. Can you remember which part of the bird you ate? Light meat or dark? Which family members were present? What they said? How many of these questions are answered because you stored discrete facts vs. recalled an image and queried it?
For these reasons, the very question of memory storage density is ill-posed. But if we agree that there is some smallest unit of recall for the human brain, then this would almost surely correspond to a vector in a Hopfield-like network. And as you can see above, the upper bound for those units is about 3 billion, for the average human brain. It may be that images require many such vectors to store, and that they are always stored with many vectors, making the total number of distinct "memories" much smaller. And some folks may object that humans can "only" store 3 billion distinct items in their head. So let me address that briefly.
Do you play tennis? How about ping pong? Can you make a complete novice into a good player using just words? No. At the very least, the novice must actually "go through the motions". The programming doesn't happen in the ears. It happens in the cerebellum. And while some folks will think of bodily-kinesthetic programming as a functional wiring of motor control circuits, there is definitely a memory capability involved. Someone who has learned to play tennis will have a leg up learning ping pong, and vice versa. That is partly because the control circuits will be wired to make similar motions, but also because the players will have memories of specific trajectories and responses which are activated in particular circumstances.
When new players play against each other for the first time, they will often perform worse than they would against a familiar person of the same skill level. That is because skill is ultimately an ad-hoc covering of the state space for the game. If the other player spins the ball or attacks in a way that hasn't been seen before, your control circuits will not have a pre-made response, even if you were physically capable of one. The conscious brain is too slow to act decisively in competitive sports. Even if you know the appropriate response cognitively, if the cerebellum has not executed the program which covers that part of the state space (including your relative position, balance, momentum, etc.), you will likely fail to produce an adequate response. Much of competitive sports boils down to remembering the best move for a particular state. Low-level programs control fine details like which muscle fibers to activate, but high-level programs like "move right while swinging across the body" must be practiced to store to memory so that it can be activated automatically in the right circumstances.
These kinds of memories generally cannot be named, and would not be thought of as discrete. They are implicit in the programming which constitutes "athletic skill". In the same way, verbal behavior can also be implicit. For instance, most English speakers can finish the phrase: "See you ____." They will generally not say "catfish" or "pulverize" or "flavorful". The fact that most speakers will finish the phrase in the same or similar way means that this bit of behavior has more to do with the mechanics of language than the personal memories of the speaker. Thus, this information is likely not stored in the pre-frontal cortex (because we know that language facility is primarily handled by Broca's and Wernick's areas). In the same way, athletic "memory" is most likely stored in the cerebellum.
I presume that you mean to exclude these kinds of "implicit memory" in your calculations. If so, then limiting the analysis to the PFC is appropriate. Otherwise, you will also need to consider the "functional" areas in the remaining portions of the brain, which is much more difficult, given that we don't have any really good models of how these work.
So, I would say that it's safe to assume that humans can "remember" much less than 3 billion distinct [personal] memories, and that the smallest chunks are on the order of 1 KB of information. That puts an upper bound of about 3 TB of information that makes you a unique history of a human. Sobering thought, huh?