Once in a while, we collect money (as a direct bank deposit) on behalf of a client and pass it through to another organization. The money collected is

If it's liability holding transaction, you may want to record as "Other Current Liability" type in QuickBooks. You may account name as you want but account type should be Other Current Liability in the Chart of Accounts.

Should I create an invoice for the client's money I'm holding to pay the organization they owe? How do I keep track of this?

Usually, you will write a check directly to the organization and the same liability account. To keep track of in and out of all the transactions, you can run the Quick Report of this specific account. From the Chart of Accounts, select liability account for this specific organization, right click it and run the QuickReport. It will show the running account balance. You can customize/memorize this report if you want.

Hope this helps!

Is this what I am supposed to do?: 

When receiving the bank deposit from client: Go to banking > Make Deposits 

In Received from: Select Client

From Account: The Other Current Liability account created

PMT Method: Bank Deposit

Amount: Record Amount

Whenever I pay the money I will write a check and choose the other current liability account again?

The money received is not income but it is a current asset in my possession. Should I create an "other current asset" and use that account when recording the deposit? Then write the check and hit the liability account?

There is a hold period. Usually less than a month. So technically the money isn't coming in the bank and leaving that same day or week. That is why I am asking if an other asset account should be created.