There's no reason to believe he remains a nonbeliever. After all, he does see Vader block blaster bolts with his hand, Luke jump higher than anyone else can and deflect blaster bolts with his saber, etc.
Dispite his inital skepticism, I think we can unequivically say that after a few years of running around with Luke, Han is a believer. He makes it pretty clear throughout the original EU (post ROTJ through NJO) that however he may feel about the philosophical and metaphysical aspects of the force, he has absolute faith in Luke's ability to do crazy $h!t with his mind!
One of his kids became a Sith Lord while another had technopathic and other abilities beyond what any force user before him had displayed. He believes.