In each case, my own preferred approach is to take the other variable into account in performing our main job of dealing with inflation and unemployment but not to target asset prices (or exchange rates). Though a consensus on exchange rate regimes may be emerging, the related issue of how exchange rates respond to monetary changes seems anything but settled.
In the textbook world of Mundell-Fleming, unanticipated monetary ease leads to lower interest rates, a drop in the home currency's value, and a stimulus to net exports. This chain of events often occurs in emerging-market countries. But there are a disconcerting number of exceptions for developed countries.