Can new employer cover COBRA?

This is a personal question for me. My husband is taking a job with a start-up and they are offering to cover the cost of COBRA until they have a healthcare plan in place. I assume this would be taxed to him as compensation with no offsetting deduction since he's an employee. Is that true? As an alternative, the start-up offered to reimburse the cost of marketplace coverage. However, if they are willing to cover the cost of COBRA, I'd rather stick with the insurance we have. Are there any pitfalls here or is the cost of COBRA just going to get added to his W-2 from the new employer? Thanks for any advice you can share with me.