Some workplaces have Employee Assistance Programs which offer certain things like legal assistance, adoption assistance, as well as counseling. It offers 10 free sessions (well "free" in the sense that the employer pays for the assistance program) and, after these free sessions are exhausted, the therapist will evaluate if you're in need of further counseling, in which case they will refer you to another therapist covered by your insurance.

Everywhere I've worked has had EAP, and I've used it a few times. Once, I just needed the 10 sessions to get through some work and school stress I was dealing with, and I found that the worksheets provided were enough to help me manage after the 10 sessions. The other time, the sessions were able to parlay into several more years with another therapist.

Edit: yes, they are qualified therapists. I actually wanted to continue seeing one of mine but he didn't take on clients in that capacity.