Can my isolation end despite having other members of my household continue to be positive for COVID-19?

Yes, each case is assessed individually.  Once you complete your isolation period as instructed by your medical provider, you can resume your daily activities. However your loved one cannot until their isolation period ends.

Source: https://www.cdc.gov/coronavirus/2019-ncov/if-you-are-sick/end-home-isolation.html; https://www.cdc.gov/coronavirus/2019-ncov/hcp/duration