Unless specific harm to the child is shown through the homosexual relationship, then there's likely to be no problem. A homosexual parent seeking custody should present evidence that the child does not witness sexual contact between the homosexual partners and that the child likes the parent's partner in order to have the strongest case.
The wishes of a child can be an important factor in deciding custody, with both heterosexual and homosexual parents. A child can often express an opinion about who he or she should primarily live with, and as long as the reason is fit, then he or she will often be put with the custody of that parent. So if the child expresses a liking to a homosexual parent and his or her partner, then there's a good chance of a favorable outcome for the homosexual parent.