Dynamic network embedding methods transform nodes in a dynamic network into low-dimensional vectors while preserving network characteristics, facilitating tasks such as node classification and community detection. Several embedding methods have been proposed to capture structural proximity among nodes in a network, where densely connected communities are preserved, while others have been proposed to preserve structural equivalence among nodes, capturing their structural roles regardless of their relative distance in the network. However, most existing methods that aim to preserve both network characteristics mainly focus on static networks and those designed for dynamic networks do not explicitly account for inter-snapshot structural properties. This paper proposes a novel unifying dynamic network embedding method that simultaneously preserves both structural proximity and equivalence while considering inter-snapshot structural relationships in a dynamic network. Specifically, to define structural equivalence in a dynamic network, we use temporal subgraphs, known as dynamic graphlets, to capture how a node's neighborhood structure evolves over time. We then introduce a temporal-structural random walk to flexibly sample time-respecting sequences of nodes, considering both their temporal proximity and similarity in evolving structures. The proposed method is evaluated using five real-world networks on node classification where it outperforms benchmark methods, showing its effectiveness and flexibility in capturing various aspects of a network.