the Provident Bank NJ They will make you lose your money, Internet

From what you described, I can definatly see why the bank is suspicious.  As there are a lot of things that are going on that would raise some "red flags".

You have two accounts to the same address.  You had an account and were apparently using his account to pay at least some of the bills.  Depending on the activity this may have triggered some additional checks. 

Then you had a money transfer to Russia.  To many banks this would be a big "red flag", as Russia is well known for various scams involving banks and money transfers.  I was to think about it based on what you have written here this is what may have put you "over the top" in having them freeze the accounts.

So they required both of you to prove you were actually who you said you were.  You brought in your ID.   Yes, they should probably have at least released your funds if the account was in your name only at that point.  However, if they do suspect fraud they may have a right to continue to hold any money in the account.  

As to your cousin, really what does bringing in a copy of his Passport do?  All that proves is that you have a copy of someone's ID, it doesn't prove that that person agreed to open the account or that you are allowed to use it.  The same goes for the call, how can you really prove that the person on the ID is the same on the phone?  Oh and like your Russian Money transfer, calling to China would also bring up some more "red flags".

What is someone opened an account in your name, had a copy of your ID and tried to pass that off at the bank.  You would probably be the first one screaming that they should have made sure that it was actually you.

At this point it seems as if they have marked your accounts as fradulent and short of having your cousin show up in person, they are not going to release the funds.  You may want to contact the Office of the Comptroller of Currency at occ.gov.  It is doubtfull that they will be able to do anything about your Cousin's account but at least they may be helpful in getting your funds released. 

"I was managing / using both accounts since my cousin was in China "

   One thing you didn't mention.   Are you an official signatory on your cousin's bank account?   If not, there's your problem.   Only the persons listed as signatories on an account can use it.  No doubt the bank's computers figured out that something was up when they started seeing transactions originating in both the U.S. and China. 

   Here's why a phone call won't work.   Right now they're looking at you as someone who may have fraudulently used your cousin's account.   A mystery phone call from China is exactly what a fraudster would suggest.