How does an HSA health plan work?

No, not that HSA

Why would you give up your copays for an HSA (health savings account) qualified plan? Let’s dive into that for a moment or two:
HSA-qualified plans give you a high deductible (anywhere from $3k-$10k for family coverage, with most people winding up around $5k) and cover 100% of charges after the deductible. (There’s none of the confusing 80/20 or 70/30 stuff with the HSA plans we sell). A key advantage is that this deductible is usually an aggregate deductible, meaning that the $5,000 deductible is a combined total for your whole family — so in any given year, no matter what happens, you’ll never pay more than $5,000 for your family’s healthcare (and here we’re assuming normal stuff, not stuff like elective plastic surgeries, etc.).
With the HSA plans, as with anything else now, you get the preventative care for free (physical, annual OBGYN, mammogram for you, etc.). Everything else has no “first dollar benefits,” which is the fancy term for benefits like doctor copays and drug copays. Instead, all of those costs count towards your deductible total (traditional copays do not count against deductibles). So you’ll pay for prescription drugs and doctors at the negotiated price (that negotiated rate is the point of a “network”), and what you pay counts towards your deductible for the year. And if you’ve reached your deductible, you won’t pay anything for the doctors or the prescriptions.
The general idea is that you’ve got catastrophic coverage to protect you from paying more than $5k in a year (or whatever deductible you choose), and you will self-insure the first $5k. To that end, you’re able to open the HSA itself (Health Savings Account). The HSA is a tax-advantaged account, meaning money you put in (up to an annual cap of slightly over $6k this year) is tax-free — you never pay taxes on that money as long as it is used to pay for health-related expenses as defined by the government. So when you pay for prescription drugs, for example, you’re doing so with tax-free money, which means your money is going further for you than it otherwise would. The savings account is yours, so if you don’t use it, it rolls over year to year until you do. Because you said your husband is technically self-employed, this tax-savings vehicle as obvious advantages.
The more traditional options that give you that drug card will come at a similar cost for the same deductible, but the deductible is per-person (usually with a max of three per year in a family) and usually includes 80/20 or 70/30 expenses above the deductible that typically rise to another $2-5,000. So your worst case scenario each year is not really $5,000 (as with our HSA example) – it’s $5,000 x 3 per family = $1500; + 80/20 of $3k x 2 per family = $6000; for a grand total of just north of $20,000! (This is a typical “copay style” plan). And you’d still be paying the doctor and drug copay after all that, and you’d lack the tax savings benefit.
Or you could take an HSA-qualified plan for a similar price. Is this the best plan for everyone? No. But for a lot of people, this Just seems like it makes a lot of sense for you all.