Household time-use patterns are expected to reflect each household member's daily activity participation and duration with intra-household interactions constrained by multiple budgets. Among various activities, the allocated activity derived from undertaking a household task is studied relatively less in the literature. Who will take an allocated activity is a discrete choice problem of household task assignment, and once a household member is assigned with one household task, other members will have more time to do other activities. To better understand household time-use patterns affected by household task assignment, this paper proposed a joint household-level multiple discrete-continuous extreme value-multinomial logit (MDCEV-MNL) model with multiple constraints. The Karush-Kuhn-Tucker (KKT) method combined with the simulation-based maximum likelihood estimation method is proposed to estimate the proposed model. Based on the household activity-travel data from Beijing of China, the proposed model is customized to explore elderly couples' time-use patterns with intra-household interactions affected by household task assignment. Following the findings, policy implications are suggested to build an age-friendly society.