I think the solution that you have already must be a schedule like the one
at the end of this topic.
This does meet your criteria. If you assign group A to the men and group B to the women, then the men and women are divided into two subgroups (1..8) and (9..16) with the same gender opponents always being taken from different subgroups.
I don't know how to construct a similar schedule such that it doesn't have this sub-group property. However, if you don't tell the participants that the sub-group structure exists, which you have assigned randomly, then I don't see that there is a big problem.
From the perspective of a single player all they will perceive is that they have been scheduled to play against 8 randomly selected players of the same gender.
As long as you only post the current round and next weeks play on the notice board, your participants are unlikely to discover the hidden structure as they would need to keep notes and compare them with one another. The mixing is still optimal in the sense that a participant's 8 partners and 16 opponents are all different.
Ian.