How do I interpret the main effect of social interaction with both interactions in the same model? Is the effect for single people (relationship status = 0) who also live alone (living arrangement = 0)?
Yes ! An interaction is interpreted as the expceted change in the outcome for a 1 unit change in the variable (or between the level of the estimate and it's reference level in the case of a categorical variable), when the othe main effect that the variable is interacted with is zero (or at it's reference level in the case of a categorical variable). So when a variable is involved in two 2-way interactions, the main effect is conditional on the main effects of the other two variables being zero (or at their refernce level. So in your case, what you wrote is correct (with a minor adjustment to make it clear we are talking about a 1 unit change in social interaction:
It is the the estimated difference in the response for a 1 unit change in social interaction for single people (relationship status = 0) who also live alone (living arrangement = 0)