Just happened to pop in and found this forum question. No, JH Studios does not give tours. You can, however, see and take pictures of the facade on La Brea, just south of Hollywood Blvd, which has a larger than life sized Kermit on top of the tower, and a painting of Charlie Chaplin at ground level, looking as though he's stepping out of the building. Theirs is a very busy, and very compact studio, with many projects going.
I recently went to Hollywood and took pictures of the facade to post on my website:
I also give general info on what to look for in studio tours, and what to look for in a tour experience. There are many that actively promote tours. Those are the ones you want. It's easy to check on studios that do offer tours. Just do an internet search. If they want tourists to visit, they'll have a site for it, I guarantee. If there is no site with tour info, likely they do not give tours. Universal, Sony, Warner Brothers, and Paramount all have large studios, and offer studio tours.
If you want to see Kermit and the gang, check out the California Adventure park at Disneyland.