1) Based on my questions and your replies, I would be suspicious of a loose hot phase conductor either inside the exterior meter socket or at the lugs on the main breaker or possibly even a problem within the local electrical utility such as at their transformer or even at the utility service entrance conductors.
2) When lights dim, this typically suggests a loose neutral issue. However, since the furnace is 240 volts as well as the range being 240 volts, both of these appliances require the 2 hot phase conductors to operate correctly.
3) Perhaps, you can borrow a volt meter from a neighbor or a friend? If not, Home Depot or Lowe's both sell AC voltmeters for $25 or less. If the power is out long enough, like say a few minutes at a time, then the voltage can be measured and confirmed at the main electrical panel. This will indicate the problem.
4) If a loose connection at the main electrical panel, I recommend to contact the local electrical utility and have them dispatch a service tech to the home. Have them confirm there are no loose connections inside the exterior meter and have them confirm their proper voltage. Most utilities do not charge for this, but you may want to confirm. You don't want to open up the exterior meter as it is against the law with most utilities as they consider it as tampering as well as for safety reasons. The other option is to contact a local licensed electrician and have them confirm the voltages.