Not to be curt, but it depends. But there were so many things not covered under the legislation that people quickly realized there were plenty of loopholes that gave insurance companies reasons not to cover mental health anyway. But many of those laws lack real teeth.
Some state laws exempt small businesses, for instance.
Many laws will allow exemptions if providing such coverage causes a company's health expenses to rise beyond a certain point. In some states, such as Nebraska, the mental health parity law applies only to group health plans, so if you have an individual plan, your rights will extend only as far as the weaker federal law. And remember, it's always wise to read your actual policy, not just your health plan summary. The policy will tell you what illnesses are covered.