First of all both species would need the same type of genetic material. The odds of that are highly unlikely at best (just look at how complex the DNA is, based on 4 distinct nucleotides with a helix structure, a highly complex system of genes, modifiers, on and off-switches etc). So they'd need the same structure, coding for genes, gene types, chromosomes, modifiers etc.
On top of that they'd need a type of genome that is compatible with each other that doesnt bring out warped and twisted monstrosities as babies, where even on earth the possibilities to get babies even between very near related races and types are small.
And last they would need some kind of almost the same type of breeding mechanism and sexuality, aside from the need of both partners to want to have a sexual relation (whatever that means for each race), if you dont want to forcebreed due to experiments.
So no, thanks, no cross breeding for me.
And no, even if I like Mass Effect alot, Asari are no good model for cross breeding in a SciFi game.