Heterogeneous Graph Neural Networks (HGNNs) could capture semantic information from graphs involving different kinds of nodes and edges. However, existing HGNNs were usually constructed without taking advantage of structural information about local graph topologies, leading to the lack of information that affects identification accuracy. Meanwhile, graph kernel strategy has been investigated to improve structural representation learning, which is primarily designed for homogeneous graphs and does not account for heterogeneous semantics. To this end, this research proposed a Heterogeneous Kernel-Enhanced Representation Network named HetKEN, which combines meta-path-guided semantic aggregation with graph kernel-based structural modeling. HetKEN firstly introduces a parameterized graph kernel layer to optimize the neighborhood structures. Then, meta-path context encoding and channel-wise meta-path fusion strategy are used to allocate the weight across different meta-paths. Finally, a cross-layer aggregation is performed to integrate multiscale information. HetKEN is evaluated on several heterogeneous graph benchmarks for node classification and link prediction, showing that it significantly outperforms the state-of-the- art work of HGNN. Experiments on six real-world datasets with six competitive methods demonstrate the effectiveness of HetKEN, which jointly employs structural and semantic information that provides more expressive heterogeneous graph learning capability.