Separate Schemas by Industry or by Application functionality?
I understand that you want to go with single database (as it is good from management &amp; maintenance point of view), but maybe it's too much integration. 

I am assuming that:


you will have separate application for each industry,
they have not very much in common (they really cover different business aspects)


I think that one of acceptable solutions in this case would be:


a separate database for each industry 
in every database, single shared public schema for shared data, including common dictionaries, all non-customer-dependent data.
one separate database user account + private schema for each customer. You might use postgres feature of table inheritance to conform to some public table.


Issues that Simon puts in his comment are really important. So you will have to enforce a very strict policy regarding GRANTs in your database.

In PostgreSQL, it is possible to achieve (as well in many other RDBMS). The key to achieving multi-tenant solution would be intelligent usage of schemas, roles, search_path setting. See http://www.postgresql.org/docs/current/static/ddl-schemas.html. Actually what I propose will in a way emulate what Oracle does. If you need help on details please ask.