Using JR Pass on Tokyo Subway/Metro Lines

Hi,

I'm going to Japan in July, first to Osaka for 5 days (including a day in Hiroshima), Kyoto for 1, then Tokyo for the remaining 7 days.

I think it would be best to use the Amazing Pass in Osaka whilst I'm there, then purchase a 7 day JR Pass to be activated the day we're going to Hiroshima. After this runs out, we won't be using the trains much in Tokyo for our last couple of days as we're going to be in Disneyland then going home.

My question really is whether I am able to use the JR pass on normal subway/metro train lines in Tokyo, or whether I'd only be able to use it on the JR lines?

I have checked all the routes I'll be using and not all use a JR line.

Thank you in advance for your help.