The joint study of double-parton scattering (DPS) in high-energy proton-proton and proton-nucleus collisions can provide a lot of information on multiparton correlations. The multiparton structure is in fact probed in different ways by DPS in p−p and in p−A collisions. In p−A collisions, the interpretation of the experimental results may be complicated, however, by the presence of interference terms, which are missing in p−p collisions. A suitable reaction channel, where interference terms are absent, is WJJ production. By studying WJJ production in p−Pb collisions, we estimate that the fraction of events due to DPS may be larger by a factor 3 or 4 as compared to p−p, while the amount of the increased fraction can give information on the importance of different correlation terms.