The Senate passed the bill by a vote of 33-1. That sends it back to the House, which had passed it 100-0 earlier.
If the House accepts changes made by the Senate, it could send the bill to Gov. Kay Ivey.
Rep. Jim Patterson, R-Meridianville, the sponsor of the bill, said he will ask the House to accept the Senate changes. Patterson said he expects that to happen on Wednesday.
Key Senate changes include making the mandate apply only to companies with at least 51 employees, making the mandate apply only to services for patients up to age 18 and delaying the mandate on public insurance plans until Dec. 31, 2018.
Patterson said he was disappointed in the delay for those plans but said overall the bill was a "victory." He said the advocacy group Autism Speaks, which has lobbied for the bill, urged him to accept the Senate changes.
Parents and advocates say applied behavior analysis can be a life-changing therapy for children with autism. But it's expensive and can be out of reach for parents if not covered by insurance.
Sen. Cam Ward, R-Alabaster, said the insurance mandate would mean that more families would be able to receive the therapy, which benefited his daughter, Riley.