Jenny, what you describe is quite possible if the flues are near each other on the roof; they're not supposed to be.
When you're burning a fire, a lot of air from the home is being drawn out; the house then has to find some way to replace that air, and it will pull it in from the easiest source first. If this happens to be your furnace flue, and the flue is next to the chimney, you'll have just what you describe.
Building Codes require a minimum distance be maintained below & to the sides of a chimney, and chimneys serving two fireplaces must have the flues offset to avoid this problem, so definitely have this looked into by a certified professional.
Not sure if they operate in your area, but if they do, a company such as HomeSafe would be a good start. You can find out if they serve your area by checking www.homesafe(your state's 2 letter abbreviation here).com, i.e. www.homesafeRI.com would be for for Rhode Island. Good luck