Content types accessible to a role
Good. I hope you are using D7.

So lets start with the finding the machine name of the permission which get saved with the user_role when you enable the permission for particular user type.

These are them - 

administer services,
get any binary files,
get own binary files,
save file information,
get a system variable,
set a system variable,
perform unlimited index queries.

Get you RID from the table ROLE by searching your NAME.ROLE

Get the list of PERMISSION from table ROLE_PERMISSION by RID.ROLE_PERMISSION

List anywhere and do what you want...

Enjoy :)