That's normal, from my understanding, unless steps are taken to isolate those big power suckers from stuff like your lights. I'm betting when they wired your house (you said it was fairly new, yes?) they saved money by either running less wires and putting more stuff on larger breakers, or they tied larger items like the furnace/HVAC into less used (but capable of handling it) breakers, which happen to be tied into a large lighting circuit.
Father-in-law installed A/C on the house, separate circuit, furnace is on a separate circuit, and no problems with those, but the built-in microwave, which shared a circuit with all the upstairs electrical, did the same thing you mention every time it turned on/off, until too much stuff was plugged in and it started blowing fuses, after which he ran another circuit, and solved the problem altogether.