Birch trees are both surface-rooted and host for aphids which secrete a bothersome honeydew that will affect plantings beneath them. You can safely plant near but not under them.

At 15 years, your birch is a mere teenager and could easily live another 50+ years.

Morz8, I don't plant any birches in my garden for that very reason. That 'bothersome honeydew' will get on cars, windows, and siding, and all plants beneath it. It may not happen in other parts of the country though.
Mike

Mike, that's a good point, I don't know that they are aphid magnets in other climates too.

That surface rooting habit on most residential size lots can be a heartache though. My mother planted birch (4!) in Longview just a little more than a couple of decades ago and they are causing her all kinds of grief now. She's 83, has damaged sidewalks, compacted beds/sparse lawn, exposed roots just waiting to trip a little old lady :(