A vertex–edge Roman {2}-dominating function on a graph G=(V,E) is a function f:V⟶{0,1,2} satisfying that, for every edge uv∈E with f(v)=f(u)=0, ∑w∈N(v)∪N(u)f(w)≥2. The weight of the function f is the sum ∑a∈Vf(a). The vertex–edge Roman {2}-domination number of G, denoted by γveR2(G), is the minimum weight of a vertex–edge Roman {2}-dominating function on G. In this work, we begin the study of vertex–edge Roman {2}-domination. We determine the exact vertex–edge Roman {2}-domination number for cycles and paths, and we provide a tight lower bound and a tight upper bound for the vertex–edge Roman {2}-domination number of trees. In addition, we prove that the decision problem associated with vertex–edge Roman {2}-domination is NP-complete for bipartite graphs.