Ladybugs will do wonders for aphids, but I'm not sure about mites. I've found one hell of a solution and I'm trying to spread the word. If you are badly infected then you need to knock them down first with some kind of spray. You can make organic pepper sprays or just get a store bought brand with pyrethrins as the active ingredient. The second piece of the solution is a pest strip with Dichlorvos. These strips will kill newly hatched eggs and provide ongoing protection from mites plus all flying insects for 4 months (unfortunately it will also kill your ladybugs).
The idea with the spray is to SATURATE! Pyrethrins is a good choice because it occurs naturally in chrysanthemum flowers and is completely organic. Mites hate moisture so you'll want to soak your ladies good right before they go to bed and let them sit during their dark period with the spray on them. Be sure to get under the leaves, a canister type sprayer works best for this. When they begin the next light cycle, spray them down with good PH balanced water only. The biggest issue here is that if you miss just one leaf, then you potentially miss dozens of mites and they will repopulate in no time. That's where Dichlorvos comes in, and man does it work.
Dichlorvos is unfortunately a toxic pesticide, but it doesn't have to come near your plants. One of these strips will protect up to 1200 cubic feet, so you can put it pretty far away and still have it effective. Hot Shot is the brand name I've seen, but there are others out there as well and the price varies between 7-15 bucks. It's not like fly paper, it just kills the bugs with some kind of toxic vapor. From what I have been able to research, it seems safe to use but is not recommended for use in bedrooms or any living areas. It needs to be enclosed in a closet or cabinet to be effective. If anyone has any ill effects from using this product please chime in!! I have used this personally and know others that have had the same results. 3 days after installing one of these and the only mites to be found are dead ones.
Good luck!!