Its a problem with your inside wiring or something attached to your inside wiring. I assum this is DSL right? do you have filters on everything? Are you using Vonage or Magic jack?
Try unplugging all your phones if you have dish unplug the recievers too. then with everything unpluged call you number and see if the internet drops you can usually just watch the DSL modem, the DSL light will go from green to red. if it doenst drop plug each device back in one at a time, call and watch the DSL modem when it drops you found the device interfering with the DSL.
Do you have an alarm? sometimes they can cause problems with DSL also.
If all this fails I would get a DSL POTS splitter and run a seperate line for the DSL modem, something like this
http://cgi.ebay.com/DSL-POTS-SPLITTER_W0QQitemZ150410954585QQcmdZViewItemQQptZPCC_Modems?hash=item2305310759