A mixed hypergraph is a triple , where X is the vertex set and each of , is a list of nonempty subsets of X, called the -edges and the -edges, respectively. A proper k-colouring of is a mapping f : X→{1,2,…,k} such that each -edge has at least two vertices of a common colour and each -edge has at least two vertices of distinct colours. If r_j is the number of partitions of X into j colour classes such that the colouring constraint is satisfied on each - and each -edge, then the vector is the chromatic spectrum of . Chromatic spectrum is broken if there exist integers i<j<k such that r_i>0 and r_k>0 but r_j=0. Mixed hypergraph is uncolourable if it admits no proper colouring. The maximum (minimum) i such that r_i≠0 is the upper (lower) chromatic number of a mixed hypergraph denoted by . In this paper we examine colourings of mixed hypergraphs in the case that is a P₃-design, i.e. a P₃-decomposition of the complete graph K_n, and construct families of uncolourable P₃-designs, P₃-designs having the chromatic spectrum broken, P₃-designs having lower and upper chromatic number equal, P₃-designs colourable only by χ and colours.