I am using the zpBase theme.

On mobile the jplayer is not responsive and the text get rendered over the jPlayer interface.

I am displaying the poster on jPlayer, if I change the sizes on the extension options it gets even worse.

I checked the style.css and jPlayer.blue.monday.css

Any tips?

You may want to try this plugin instead:
https://github.com/acrylian/mediaelementjs_player

Thanks, WIll give it try.

Ok, awesome player, but it still does render properly on mobile. The bottom text is redered over the player.

Seems to be theme styling issue.

Yeah, it's a very complex theme. You may want to un-check the Vertical Scale Full Image theme option and see if that suits you.

If you like to use jPlayer you should try our own included skins for it. Those are at least basically responsive. Sadly jPlayer by default is not and it is quite hard to style otherwise.