We show a new invariance principle for the radius and other functionals of a class of conditioned `Boltzmann-Gibbs'-distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in [jfmgm05]. As in the latter paper, we make use of a bijection between planar maps and a class of labelled multitype trees, due to [BdFGmobiles]. We also rely on an invariance principle for multitype spatial Galton-Watson trees, which is proved in a companion paper.