In landline connections, commonly a land phone will be connected along with the modem in the same line.
When using the internet, a voice call interrupt to the modem disconnects the internet and steady DSL will loss , it can maintain a steady DSL (Digital subscriber line) only after the end of a voice call. Any chance of such interrupts disconnects the DSL when phone rings. If the connection in the line is improper or any defect in splitters/filters or something result in disconnection of DSL or dialup in the modem while the phone rings or use. In order to fix this you should ensure the connection is in proper way using filters/splitters, this problem can't be fixed in the absence of a filter.
Normally in landline broadband an ADSL filter/splitter is used in the line, where the line split into two, i.e one connection to modem and other to the telephone. Make sure the cables to modem and telephone are taken from the correct sockets in splitter as indicated in it (An image of telephone and computer will be marked for to identify plug) and then make sure the filter used is the right type. Also the splitter should be placed before telephone i.e, the splitter should be next to the junction box or next to the jack.Placement of splitter after a telephone line splitting have no effect and also multiple filter in the line cause attenuation of the signal, also results in DSL disconnecting.
If the problem persists even after the fixing of all the above mentioned, check whether the ADSL splitter is working properly, it has a high chance of damage as they have poor life and easily affected by lightning. Frequent checking and replacing of filters are most recommended, as the internet speed and DSL stability are affected seriously by filters. Try it by replacing the filter.Also the distance of the wiring and signal strength also account for DSL stability, because a considerable attenuation occurs at the transmission line too.If the problem still remains contact your ISP for technical assistance and line maintenance.