Birth control pills increase sexual hormone-binding globulin (SHBG), which means more of your sexual hormones are being bound (including testosterone, which controls body hair, acne, and sex drive). When the hormones are bound, they are not as easily utilized/absorbed (not too sure how this works). So this means that your body isn't using the testosterone it is making as it normally would. Pros: less acne, less body hair. Cons: loss of sex drive.
The progestin in Microgestin Fe is norethindrone actetate, a relatively non-androgenic (low in testosterone) progestin.
You could try to find an aphrodisiac that is compatable with birth control (I am trying to find one myself). I believe that when they did studies, the Patch didn't have as much of an effect on SHBG as the combined pill did, so you could try that. If you were to switch to a different pill, hypothetically you could switch to one with more androgenic activity containing either levonorgestrel or dl-norgestrel. Pills that contain these progestins are: Alesse, Levlite, Levlen, Levora, Nordette, Lo/Ovral, Triphasil, Tri-Levlen, Trivora, and Ovral.
As for the depression, you will want a pill with lower progestin potentcy. Microgestin has 1.5 mg of norethindrone acetate, which equates to 1.8 mg of norethindrone, a pretty high dose of progestins. Avoid triphasic pills (packs with different hormone levels every week) as these can cause depression, so that eliminates Triphasil, trivora, and tri-levlen, which leaves us with Alesse, Levlite, Levlen, Levora, Nordette, Lo/Ovral, and Ovral. Microgestin has 30 mcg of estrogen, so we will look for a pill with a similiar level of estrogen that is low in progestin, which has some androgenic activity. Hang on... Keep in mind that your bc has an equivalent to 1.8 mg of norethindrone.
Alesse (20 mcg of estrogen, 0.1 mg of levonorgestrel which equates to 0.53 mg of norethindrone )
Levlite (similiar to above),
Nordette (30 mcg of estrogen, same dose you are on now, with 0.15 mg of levonorgestrel, which equates to .795 mg of norethindrone)
Overall, I would suggest Nordette, because it is the same estrogen level you were on before but it has less than half the progestins of Microgestin (which will help with depression), and is more potent in androgen so it will hopefully help with sex drive too.