The relationship between nodes and edges is always undirected. If you need properties on the connection between node and edge, you're effectively elevating those connections to edges themselves, so you have one group of nodes (the original nodes), another group of nodes (the former hyperedges) and finally the edges between nodes of the two types, which can then be directed.
If you say, no, you need a particular property of this being a hypergraph, it would be interesting to learn what that is!