Federated Instruction Tuning (FIT) advances collaborative training on decentralized data, crucially enhancing model's capability and safeguarding data privacy. However, existing FIT methods are dedicated to handling data heterogeneity across different clients (i.e., client-aware data heterogeneity), while ignoring the variation between data from different domains (i.e., domain-aware data heterogeneity). When scarce data needs supplementation from related fields, these methods lack the ability to handle domain heterogeneity in cross-domain training. This leads to domain-information catastrophic forgetting in collaborative training and therefore makes model perform sub-optimally on the individual domain. To address this issue, we introduce DoFIT, a new Domain-aware FIT framework that alleviates catastrophic forgetting through two new designs. First, to reduce interference information from the other domain, DoFIT finely aggregates overlapping weights across domains on the inter-domain server side. Second, to retain more domain information, DoFIT initializes intra-domain weights by incorporating inter-domain information into a less-conflicted parameter space. Experimental results on diverse datasets consistently demonstrate that DoFIT excels in cross-domain collaborative training and exhibits significant advantages over conventional FIT methods in alleviating catastrophic forgetting. Code is available at this link.