unemployment goes up. As economy slowly improves, people start returning to job searching increasing the pool of people looking for jobs, and due to lag of search to on-job, unemployment rate increases.
Interest rates and unemployment changes will be dampened, I think. As the economy improves, more people will enter the workforce - causing the reported unemployment rate to increase (or decrease less). Without the decrease in labor force from 2008-2012, unemployment would be what? 9%?
The Fed has explicitly stated that they will maintain low rates until unemployment is at 6.9% or less. So, we will be stuck for a while in this environment with high unemployment and low rates, even as the economy improves (along with stock prices).