This is about a fictional planet that has a solid land surface but on which the atmosphere is composed of some liquid containing hemoglobin, or some artificial blood substitute.
I am not sure yet if the planet could have any kind of ocean. So perhaps instead of an ocean it would be covered by the liquid atmosphere.
Could humans breathe on such a planet?
Not easily.
Hemoglobin wants to bind to Oxygen. That's how it pulls it out of the air to be distributed to our cells. However it generally doesn't pass across the surface of the aveoli in our lungs. If it did, we'd drown to death in our own red blood cells. In your situation, you'd have hemoglobin in the aveoli from the atmosphere, and hemoglobin in the bloodstream. There is no way for them to trade places, so the only way for oxygen to travel across the boundary is through osmosis.
However, now we have hemoglobin on both sides, instead of hemoglobin on one side and free oxygen on the other. There is no longer any chemical advantage to moving oxygen across the barrier, so all we get is weak diffusion. The rate of exchange would be far lower.
If you wanted this liquid air planet to work, you would need to choose a hemoglobin like molecule which has much less affinity for oxygen than hemoglobin does. That way there would be some chemical advantage to moving oxygen from one molecule to another.
The last question would be the physical costs of breathing liquid, and how hard it could be on the lungs, but I think that's a separate question to be answered.
There is the possibility of Liquid Breathing, however it is unlikely that the liquid would be haemoglobin and still be breathable, as haemoglobin is quite viscous (this is why it is contained within red blood cells).
On the other hand, in the unlikely event that a planet was completely covered by an ocean of some largely colourless oxygen saturated liquid such as a flurocarbon at ~37°C, then, yes, humans could in theory breathe this liquid. It is probable that if such a planet existed, it would have been manufactured by some powerful civilisation.
However, free-breathing fluorocarbons is exhausting due to the mass of fluid involved and the amount of oxygen that could be saturated in it. Were humans to spend any length of time in such an environment, it is likely that they would need some sort of mechanical breathing assistance to prevent exhaustion.
Finally, fluorocarbons are up to twice as dense as water. This means that a human would float on the surface of a fluorocarbon sea to a greater degree than in highly saline water (such as the dead sea). However, with the mechanical assistance required for prolonged breathing and movement, neutral buoyancy could be achieved.
Finally, if this world had any significant amount of water, since flurocarbons do not mix to any great extent with water, any of the world's free water that could not dissolve in the fluorocarbon sea would likely form a layer on top of the fluorocarbon layer, over which would be any gaseous atmosphere.
The main question in this world would be how the fluorocarbon sea maintained its oxygenation.
