If your employer pays 100% of the employee cost of their group health insurance plan (very rare these days) then you will be enrolled in your employer’s health plan. That doesn’t mean you have to use it or that you couldn’t be covered as a dependent on your spouse’s health plan.
If an employee contribution is required under your employer’s plan (extremely common these days) then you are free to “waive participation” (i.e. – elect not to be covered) in your employer’s plan and can be covered under your spouse’s plan.
Generally, unless there is a significant benefit difference involved between the two plans, (and I’m assuming it’s just you and your spouse and there are no children involved) it would probably be less expensive for each of you to be covered as Employee Only under your respective employer’s health plans.
Another important note is that one of the quirks of the Affordable Care Act (ObamaCare) is that spouses weren’t defined as dependents (no reason has ever been given for this). This has led a few employers to not offer coverage to spouses at all, but this is still very rare. What is becoming increasingly common though is an employer policy that penalizes spouses who elect to be covered under their spouse’s employer’s plan when that spouse has health insurance available at their place of employment. Usually a higher monthly premium payment is assessed for such a spouse as opposed to a spouse who does not have other health insurance available. You’ll want to make sure your spouse’s employer doesn’t have such a personnel policy in place before you opt to be covered under your spouse’s health plan.