Summary: Let \(F\), \(G\), and \(H\) be multigraphs. An \((F,G)\)-decomposition of \(H\) is an edge decomposition of \(H\) into copies of \(F\) and \(G\) using at least one of each. For subgraphs \(L\) and \(R\) of \(H\), an \((F,G)\)-packing of \(H\) with leave \(L\) is an \((F,G)\)-decomposition of \(H-E(L)\), and an \((F,G)\)-covering of \(H\) with padding \(R\) is an \((F,G)\)-decomposition of \(H+E(R)\). A maximum \((F,G)\)-packing of \(H\) is an \((F,G)\)-packing of \(H\) with a minimum leave. A minimum \((F,G)\)-covering of \(H\) is an \((F,G)\)-covering of \(H\) with a minimum padding. Let \(k\) be a positive integer. A \(k\)-path, denoted by \(P_k\), is a path on \(k\) vertices. A \(k\)-star, denoted by \(S_k\), is a star with \(k\) edges. In this paper, we obtain a maximum \((P_{k+1},S_{k})\)-packing of \(\lambda K_n\), which has a leave of size \(< k\), and a minimum \((P_{k+1},S_{k})\)-covering of \(\lambda K_n\), which has a padding of size \(< k\). A similar result for \(\lambda K_{n,n}\) is also obtained. As corollaries, necessary and sufficient conditions for the existence of \((P_{k+1},S_k)\)-decompositions of both \(\lambda K_n\) and \(\lambda K_{n,n}\) are given.