This interference is unfortunately quite typical as David pointed out in his comment.
A typical household microwave oven operates at 2.45 GHz, the 802.11g wireless spectrum lies in the range of 2.412 to 2.472 GHz. This by itself is not a big problem, as the WiFi algorithms use sophisticated algorithms to operate even with noise at the same frequencies. The problem is the leaked power that can be much higher than any nearby WiFi signal. The shielding is never perfect and usually from the ~800W only a tiny amount will leak out through the seals, the metallic grid in the front window, etc.
We analysed the amount of leakage with a calibrated microwave sender/receiver pair during my undergraduate time and found attenuation in the range of 99.75% to 99.98% for different types of metallic grids in the front doors. This means that still 160mW to 2W can leak out of the oven (I am not sure if 2W of leakage are even allowed today as it was an old microwave oven). Compared to the allowed output power of WiFi of 100mW to 300mW depending on the region/country it is easy to see why a not well shielded oven can drown out the signal completely. You can avoid the WiFi interruptions by trying out different channels, using a 5GHz setup or using a better microwave.
The biological harm caused my microwave radiation is still under debate to phrase it mildly. There a lots of different effects and long-term influences are very hard to characterize. So if we take the worst case scenario of the 2W leaking microwave it is safe to assume that any thermal effects are tiny as you will not put your head against the oven and from the distance of a couple of centimeters the deposited power per volume is too small to have any effect. The same cannot be said so easily for a cellphone which you have for a long time very close to your head, but after hundreds of studies it is clear that immediate negative effects could not be found and now big long term studies try to characterize effects that only happen after years of exposure.