Harmonic state estimation in distribution networks is essential for identifying harmonic sources. However, issues such as limited measurement redundancy, asynchronous measurements, and unbalanced load distributions in three-phase networks undermine the reliability of existing methods in practical applications. To address these issues, this paper proposes an interval harmonic state estimation method in three-phase unbalanced distribution networks, integrating data from multiple sources. First, the interval multi-source harmonic measurement dataset is constructed by integrating asynchronous harmonic measurement data from multiple sources. The time asynchrony of measurement data from power quality monitoring devices is calibrated using the sliding window weighted dynamic time warping algorithm. Second, the interval harmonic state estimation model for the three-phase asymmetric distribution network is constructed. The model is solved using the interval-weighted least squares method, enhanced by the improved Krawczyk operator, thereby minimizing the expansion resulting from interval operations. Finally, the feasibility and accuracy of the proposed interval harmonic state estimation method are validated.