If I was hit by a commercial vehicle in a Florida car accident, is the employer of of the other driver also responsible?

If the employee was acting within the course and scope of his employment when the accident occurred, then yes. For example, if the driver was a driver for a florist and making a delivery of flowers, and he was making a delivery at the time of the accident, then the florist would be responsible for your injuries in addition to the at-fault driver.