Given the 12 round limit, I would look to have 16 players, 8 males and 8 females. There needs to be a total of 32 games in order for all men to partner all women exactly once, and these can be arranged in 10 full rounds that use all three nets and one short round with only two nets.
Net 1 Net 2 Net 3 Byes
(M2 F3 : M6 F5) (M3 F2 : M7 F1) (M5 F7 : M8 F6) (M1 M4 F4 F8)
(M1 F8 : M2 F1) (M3 F5 : M5 F6) (M4 F3 : M8 F7) (M6 M7 F2 F4)
(M1 F5 : M6 F7) (M3 F6 : M4 F8) (M7 F2 : M8 F1) (M2 M5 F3 F4)
(M1 F7 : M3 F8) (M4 F6 : M6 F1) (M5 F3 : M7 F4) (M2 M8 F2 F5)
(M2 F7 : M5 F1) (M3 F3 : M4 F4) (M6 F6 : M8 F2) (M1 M7 F5 F8)
(M2 F4 : M4 F2) (M3 F1 : M6 F3) (M7 F5 : M8 F8) (M1 M5 F6 F7)
(M1 F1 : M8 F4) (M2 F5 : M7 F6) (M5 F8 : M6 F2) (M3 M4 F3 F7)
(M1 F3 : M5 F2) (M3 F4 : M8 F5) (M4 F7 : M7 F8) (M2 M6 F1 F6)
(M1 F2 : M4 F5) (M2 F8 : M8 F3) (M6 F4 : M7 F7) (M3 M5 F1 F6)
(M1 F6 : M7 F3) (M2 F2 : M3 F7) (M5 F4 : M6 F8) (M4 M8 F1 F5)
(M1 F4 : M2 F6) (M4 F1 : M5 F5) (M3 M6 M7 M8 F2 F3 F7 F8)
Each player gets exactly 8 games and 3 byes. I have no way of optimizing the schedule for the distribution of the byes, so you might like to consider playing the rounds in a different order as above F1 and F4 have all their byes back-to-back.
Hope that helps.
