According to WP:
The number of deaths per passenger-mile on commercial airlines in the United States between 2000 and 2010 was about 0.2 deaths per 10 billion passenger-miles
The ISS is by far the largest contributor to crewed spaceflight time in the 21st century, being continuously occupied by 3-6 people for over 17 years since November of 2000, during which time it's achieved somewhere between 8 and 16 billion passenger miles†. Shuttle flights from 2000-2011 make up something like 10% as much as that; Soyuz flights are accounted for by my ISS crew estimate, and other crewed spaceflight missions are negligible.
Over the same time frame, 7 astronauts have died (the crew of Columbia on STS-107).
That makes space travel about 20-40 times more dangerous than airline travel by passenger-mile, but it's worth noting that all the astronaut fatalities in the 21st century occurred in that single incident, so we're clearly dealing with statistical outliers here; the "real" hazard rate could be much higher or much lower. In the decade 1991-2000, there were no astronaut deaths, making space flight infinitely safer than air travel; in the decade 1981-1990, there were 7 deaths in the single Challenger incident with far fewer space-crew miles flown to amortize over.
As Hobbes notes, it might be more appropriate to consider the risk by passenger-hour rather than by passenger-mile. In this case, assuming an average of 500 mph for airlines, we get ~0.01 deaths per million passenger-hours. There have been somewhere between 500,000 and 1 million passenger-hours spent on ISS, and again 7 deaths. This makes space travel 700-1400 times as deadly per passenger hour.
† 26500 miles per orbit * 1440 minutes per day * 6360 days / 92.65 minutes per orbit = 2.6 billion miles per crew member.