wow, there is a lot of confusion going back and forth here.
All humans have roughly the same number of chromosomes and genes. There is variation between populations and individuals, and there are genetic disorders which change the total number of genes, and which are usually detrimental - often fatal. In most humans, however, there are 24 chromosome pairs, for a total of (very roughly) 3,000,000,000 base DNA pairs.
Individuals and populations can have different alleles and different versions of genes coding for different traits, but by and large, we have very very similar DNA.
When a phenotype change occurs in a population (e.g. an average darkening of the skin) that can happen in a number of places inclusively between DNA and the skin pigment itself.
1) The length of time pigment proteins are allowed to exist once created. Every protein in the body has a shelf-life, and is destroyed after a while. The longer a given type of protein hangs around, the more of it can accumulate.
2) The length of time tRNA hans around. m- and t-RNA are in charge of actually building proteins from genetic code, in a process called transcription. Then longer these molecules hang around, the more work they end up doing.
4) Expression of RNA - once the RNA is created, it can be expressed or not. I'm not as familiar with th current understanding of how this is regulated, so I won't try to explain this
5) Expression of DNA - recent studies suggest that even the "dormant" DNA, sections that do not result in protein formation, are still partially translated into RNA. During this process, however, the RNA is not completed, and with the job half done, the RNA doesn't produce any proteins, and so the DNa is not "expressed".
Now if a mutation to an active DNA region occurs (a genotype change), and it actually has an effect on the resulting proteins (many mutations have no protein coding effect *at all*), then it either shuts off protein creation, reduces protein creation, increases protein creation, or it alters the protein itself.
During the long isolations of human populations in the past tens of thousands of years, certain groups have seen collections of genetic mutations unique to their groups. So an Asian man will have genetic characteristics not found in African or European men, and vise versa.
Those genetically encoded changes (as opposed to expression changes based on environmental factors) do not exist everywhere, and so no, an African couple cannot produce an Asian child. The gene versions are not present for that to be possible.
HOWEVER, there is more genetic variation between individuals than there is between "races", so this is no different than saying that two people with green eyes (recessive trait) cannot have a child with brown eyes. nor is it claiming any significant value in dividing people into groups based on skin color or skeletal structure.
http://en.wikipedia.org/wiki/Dominance_relationship
valich is correct, though I would in a large part disagree with Idle Mind's assertion that a surrogate mother of a different race would in any significant measure effect the fetus. Barring conflicts like rH factor between mother and child, the placenta provides a fairly good barrier between the two distinct living organisms.