I also think you could have 100% genetic diversity, but not as Philip suggests, since you are looking for the male and female to be of the same species.
Jason K gave you a good answer, but I would like to expand it even further.
Now, the example I'm about to give you is just theoretical. There is not, to my knowledge, anything like it on the real world.
Humans have 46 chromosomes on each cell, which constitute the totality of their genetic code. There is 1 pair of sexual chromosomes (XX in women and XY in men) and 22 pairs of other chromosomes (these are named autosomal and code everything else in the body).
Let's assume a species with the same genetic configuration, but in which male and female are so diferent, they look like diferent species.
First, you must know that, although we have a genetic code, not all genes are expressed all the time. Some are up-regulated and some are down-regulated. Which means, some genes are activated and some genes are inactivated. A liver cell will express a diferent set of genes than a brain cell, even though the genetic code in both is the same.
Now, imagine that each member of that species has
- 2 sexual chromosomes, that determine the individual's sex
(let's call them S chromosomes)
- 22 chromosomes that contain genes for a male member of the species
(let's call them M chromosomes)
- 22 chromosomes that contain genes for a female member of the species
(let's call them F chromosomes)
The S chromosomes would determine if the individual would be a male or a female. How? The S chromosomes of a male would "silence" the F chromosomes. And the S chromosomes of a female would "silence" the M chromosomes.
So, a male would only express the genes from the 22 M chromosomes and a female would only express the genes from the 22 F chromosomes.
This means that the content of the M and F chromosomes could be completely diferent. The only thing that would have to remain equal for both sexes would be characteristics that would allow genital and environmental compatibility, so that males and females could reproduce.
What about the genetics of reproduction?
In humans, the gametes contain half of the totality of the genetic code, ie 23 chromosomes (being 1 sexual and the other 22 autosomal).
When the 23 chromosomes from a sperm combine with the 23 chromosomes of the ovum, we get 46 chromosomes again: this is a new individual.
In your fictitious species, you would have to work this out a little further, lest a male individual gets a majority of F chromosomes (and vice-versa), which would be incompatible with life.
In the production of the gametes of your species, you would need them to contain:
- 1 S chromosome
- 11 autosomal M chromosomes
- 11 autosomal F chromosomes
When the gametes combined, this would render 46 chromosomes again:
- 1 S chromosome from the father + 11 M chromosomes from the father + 11 F chromosomes from the father
- 1 S chromosome from the mother + 11 M chromosomes from the mother + 11 F chromosomes from the mother
In this way, you would ensure genetic diversity because a female daughter wouldn't get all her F chromosomes from her mother, but rather half from her mother and half from her father (yes, the father would transmit half of his own inactivated F chromosomes). You would also ensure that every member of the species would have the set of chromosomes required for their assigned sex.
So, it is theoretically possible to have 100% genetic diversity, since the genes expressed in both sexes would be completely diferent. Even though, of course, there would not be so much genetic diversity if you took the genetic code as a whole.