  We first rephrase and unify known bijections between bipartite plane maps and
labelled trees with the formalism of looptrees, which we argue to be both more
relevant and technically simpler since the geometry of a looptree is explicitly
encoded by the depth-first walk (or {\L}ukasiewicz path) of the tree, as
opposed to the height or contour process for the tree. We then construct
continuum analogues associated with any c\`adl\`ag path with no negative jump
and derive several invariance principles. We especially focus on uniformly
random looptrees and maps with prescribed face degrees and study their scaling
limits in the presence of macroscopic faces, which complements a previous work
in the case of no large faces. The limits (along subsequences for maps) form
new families of random metric measured spaces related to processes with
exchangeable increments with no negative jumps and our results generalise
previous works which concerned the Brownian and stable L\'evy bridges.
