Where do you live and what do you do in the military? That can really help determine where you can get a good job with good benefits.
Before you even interview for a job ask them about their insurance. Some key things to find out: how long before pre-exhisting conditions are covered? Are there co-pays for doctor visits and persriptions? If so, how much? Is there a deductible and how much? What percentage of typical doc visits and procedures is covered? Do you need referals to see a specialist?
All of these things can help you determine how much of a hassle you might have with a company and how big your bills might be. If you look at your explanation of benefits statements from tri-care you can get a good idea of how much yours and you kids healthcare will cost you. For example if only 80% of doc visits are covered and a typical clinic visit runs $1000 then that leaves you with $200, plus any co-pays and deductible.
You can also find out if they have a plan for you to put away money pre-tax for health care. The only catch with these is that you have to use all the money you save before the end of the year or you lose it.
How long before you get out of the military? I would get your kids into the doctor and stock them up on their meds right before you get out just in case there is a long waiting for pre-exhisting condition coverage. In my experience it is usually 3 months.