Most U.S. health insurance is provided as an employment benefit, by our employers. We may or may not pay a portion of the cost (premium); that is a decision each employer makes. If we do pay all or part of the premium, it is deducted from our paycheck.
We also have privately obtained health insurance that is paid in full by the insured person.

Coverage varies by policy. Some benefits are generous and some are limited. Recent laws have been passed to try to ensure that mental health benefits are provided and are reimbursed at the same rate as medical health benefits.

Depending on the type of policy, benefits may be a percentage of the amount the insurance company determines is the maximum billable (allowed) amount, paid only after a large annual deductible has been satisfied (up to $2,000.00). With this type of policy, a person pays all costs until the deductible is reached; the person may never receive benefits during the year because the large deductible isn't reached. When the deductible is reached, then the person would pay a percentage of the allowed amount - for example 20%.
Or, with another type of insurance policy, the benefits may be payable at maximum allowed amount, minus a specific dollar amount that is the patient's responsibility ($20 or $30 co-pay, for example. The co-pay can be any amount).

An insurance policy is merely a legal contract between the parties involved: the insurance company, the employer or purchaser, and often the providers (who are contracted to perform care at a specific price), so there can be a wide range of types of policies and of the benefits the policies provide.

So, when you change jobs here, you usually change insurance policies also. You may end up with a better policy with good benefits, a wide range of providers (doctors, hospitals, pharmacies, etc) that you can use and at a low cost ... or you may end up with a policy that is more restrictive in the kind of benefits provided, a higher cost, fewer providers to choose from, requirements for obtaining approval before seeking certain types of care (including mental health).

I hope this helps!