This sounds very close to a retainer style agreement, but with payments in arrears. I don't like this.
If you and the client know that it will cost $xxx of money every month, it should be due by the 1st of each month, in advance. That would make it a proper retainer. You need an agreement in place (contract, Scope of Work, etc) to protect you, and the client. Even if the client is big, you should not be bullied around. Period.
I would recommend getting a proper retainer contract drawn up with a lawyer, and making sure issues like this will not happen again. For example, how does one party end the contract? What happens if payment is not made? What happens if they want you working more than what is in your retainer account? A lawyer will get all this written down, in plain Legalese writing, and explain in detail what you are signing with your client. In my experience, I only do this type of arrangement with 2 very good clients, and it does include a lot of reasonable restrictions. See this answer for what I do and suggest.
In short, you need these terms worked out ahead of time. After work has started, you may only be going on the client's good word that you'll get paid, and on time. Every time you do something for a client, it needs to be billed out; whether it's once a month, or as you leave their site each day. On the invoice, it should state your payment terms, and it should be clear before working for the client.
Since you already did the work and billed the client, you are currently waiting for the money to come in. I would suggest getting the contract (as suggested above) drawn up, ready to sign with the client. Schedule a meeting to talk to the client, and explain (very calmly!) your concerns about payment, and the work you are doing. Make sure you never put down the client, but that he respects you as you respect him. If he is being rude, interrupting when you are speaking, etc., then I would just leave the client; you may try another day if you feel that would help.
When dealing with businesses, they have their own practices. If they do not work for your company, you need to address that with them, and potentially reach a compromise with them. Remember, they are paying for your expertise, and they expect to get their money's worth. They need to feel as though they are in charge, and that you are there just to guide them and complete anything they can't/won't themselves. I would start the conversation slowly and softly, and explain that you do like this working relationship, but would like to see the money a little quicker. It will be a touchy subject for most clients, so please don't beat around the bush to talk to them.
Now, do I feel you are in the right for calling and asking about the money owed, after only 15 days? I'm on the fence. I believe I need to get paid in a timely manner, but I also send out the bill every day, as soon as the work is done. My terms are set to Net 30, so I don't even think about the bill until the next month. Usually, I set aside the 1st of each month to go through "overdue" bills, and just send a friendly reminder. After 60 days, I add 2%, compounded monthly. I have not gotten to 90 days yet, as the 2% late fee after 60 days gets the money almost right away.
Hope this helps, and do realize, this may be a touchy subject. Don't beat around the bush, respect them in your conversations, and understand their point of view (i.e. Joe Freelancer wants money quicker than usual for some reason).