In the past few years, higher-order community detection has drawn an increasing amount of attention. Compared with the lower-order approaches that rely on the connectivity pattern of individual nodes and edges, the higher-order approaches discover communities by leveraging the higher-order connectivity pattern via constructing a motif-based hypergraph. Despite success in capturing the building blocks of complex networks, recent study has shown that the higher-order approaches unavoidably suffer from the hypergraph fragmentation issue. Although an edge enhancement strategy has been designed previously to address this issue, adding additional edges may corrupt the original lower-order connectivity pattern. To this end, this paper defines a new problem of community detection, namely hybrid-order community detection, which aims to discover communities by simultaneously leveraging the lower-order connectivity pattern and the higherorder connectivity pattern. For addressing this new problem, a new Micro-unit Modularity (MuMod) approach is designed. The basic idea lies in constructing a micro-unit connection network, where both of the lower-order connectivity pattern and the higher-order connectivity pattern are utilized. And then a new micro-unit modularity model is proposed for generating the micro-unit groups, from which the overlapping community structure of the original network can be derived. Extensive experiments are conducted on five real-world networks. Comparison results with twelve existing approaches confirm the effectiveness of the proposed method.