New Freelancer: Payment Terms

I am a web dev with almost 8 years experience and recently started freelancing on the side. I have had my first client for about a month now, just doing some maintenance on a single site.

I recently conducted a review on the code base for the site and came up with about 50-60 hours of enhancements. We originally agreed to work on an hourly basis and the expectation of about 5 hours of work per month. They agreed to pay me at the end of each month and they also thought some project work would come up.

Today, they agreed to the enhancements I recommended. They want all the work completed as one deliverable, but are proposing that they pay for three line items as monthly maintenance (they are roughly 5 hours each) over the course of the next three months. All other items are to be paid as they are completed.

Is this scenario considered standard practice? I have yet to receive payment for the first invoice, due on the 15th. I am a bit uncomfortable delivering without being paid for a month or two at a time. Advice is greatly appreciated!