Dunno why you think j.p is good at all against her. I play this matchup on a daily basis. At most it nets you a 20% combo into kd that you really won't be getting that often. If Millia is airborne she's coming down with either a pin, j.k, or a long range j.d. The right spacing eats j.p most of the time. J.k and pin = free combo into a corner and j.d also nets a knockdown. I mean is she supposed to be jumping around and not blocking or something, I don't get why anyone would eat that. Even iad pin shuts that down. In general Millia at close range in the air isn't really good against anyone if she's really low, she eats a lot of shit if people jump at her, so at a close range it may be okay to j.p, but I wouldn't count on anyone being dumb enough to put themselves in that position. Anybody with decent spacing and Millia playing experience won't eat that except from Ky or some shit.
Being airborne while MI is airborne is good because it's harder for her to turn stuff that isn't a counter hit into a combo, it's harder to adjust to a character that decided to jump and block pin air to air, there are times when you can get a free grab just from blocking pin air to air, and at a long range it's a little harder to aim pin imo. Also if you're above her while air to air it's even better (if you jumped after she's already taken flight or been in flight) because pin becomes useless, j.p and j.s are aimed down, j.k and j.d won't work as well either, and Sol's j.h is good in general.
J.h is amazing air to air I will admit. That shit eats pin for free on startup and is amazingly hard to grab, I don't remember the last time i was able to beat it. If you ever get her into a position where she has to tech, just mash on j.h imo, she can tech and throw out pin if she wants but it won't even fucking come out. Though if you do get retarded with it a random air fb disc will eat you alive.
As for Sol on the offensive. You say air attacks are good at a close range. Idk what you mean when you say it but 2H eats his j.h for free and trades in her favor. It also beats bandit revolver. 6p shits on everything else. If she gets greedy with the 6p AA, just bait it. The recovery is really slow and you'll pretty much get a 40 percent combo at least. Also if you're jumping around with j.h or you iad with it and end up on the opposite side of her, she gets a free 5p into combo out of it. She also has roll that gets her out of stuff for free and she has fb disc that she can set and return the game to neutral or her favor.
I agree 100 percent with the rest of your post.
Some stuff I wanna add though.
FB disc. If it's out and you're down in the corner, you got 50 percent tension. Don't take a chance with VV. It goes through it completely if you connect, but if you don't and your rc it you're still back to blocking. Go for Grand Viper instead. It goes under it and puts her into a position where she has to start blocking your pressure. It also catches her if she decides to backdash and 6k to bait your VV. I don't remember what happens with badmoon vs GV though.
If she's ending strings with h disc and wants to get pretty and rush you because you're still blocking, just 2D her. If FB disc is ever dropped when you're jumping in and you end up doing an empty jump but not too close to where she can grab you, you just go for command grab. Same thing goes for if she sets a fb disc at neutral and you're rushing her down. Just go for keep going and wild throw before it's active.
Don't do anything dumb and mash out normals just because you have them. Maybe 2s but that's it. Empty gunflame is also no good. MI gets in for free if you don't RC it. Occasionally you can get free jump outs of H disc oki just because you have a dp.
If you score a kd it's not really too good of an idea to go for Sol's AD oki because I think Millia can just roll under it. She also rolls past BB and BR (though she should be using 2H vs BR). Sol's dust is pretty garbage, you miss it close range and MI has 50 percent tension, it's 5s > 5h > into Emerald Rain overdrive.
Midscreen oki mixups like iad over and back and roll also bait wakeup VV. Sol's 5k is really gay and will beat pin startup at close range. Usually I'll just fd on the way down or something, I'd rather take my chances getting air thrown than eating 5k into sidewinder loop. If you block tk badmoon, go for a command grab, the MI player already knows she's at a frame disadvantage.
If you play a patient SO vs MI you won't really have too much of a problem. She still gets to dance around and play as safe as she wants to because it's so hard for Sol to catch her and keep the pressure on, but at the same time you won't be giving her too many chances to screw you off. You can take a few chances obviously, just don't be dumb about it.
That's it for now.
