In a two-layer quasi-geostrophic model, the interaction between two opposite-signed hetons (baroclinic vortex pairs) is studied analytically and numerically, for singular and finite-area vortices. For point vortices, using trilinear coordinates, it is shown that the possible evolutions depend on the deformation radius Rd: for large Rd, the layers decouple, vortices pair in each layer and their trajectories are open; for medium Rd, the exchange of opposite-sign partners between layers becomes possible; for small Rd, two other regimes appear: one where hetons remain unaltered during their evolution but follow open trajectories, and one where hetons occupy only a bounded subdomain of space at all times. Conditions for invariant co-rotation of the heton pair are derived and analyzed. Then, the nonlinear evolutions of finite-area heton pairs, with piecewise-constant vorticity, are computed with contour dynamics. When the central cyclonic vortex is initially aligned vertically, a transition occurs between three nonlinear regimes as layer coupling increases: for weak coupling, the vortices pair horizontally and drift away in opposite directions; for moderate layer coupling, the core vortex splits into two parts, one of which remains as a tilted columnar vortex at the center; for stronger layer coupling, each anticyclone pairs with part of the cyclone in each layer, thus forming an L-shaped dipole, a new coherent structure of two-layer flows. When the initial distance between the central and satellite vortices is increased, the velocity shear at the center decreases and the central vortex remains vertically aligned, thus forming a Z-shaped tripole, also a newly observed vortex compound. Such tripoles also compete with oscillating states, in which the core vortex periodically aligns and tilts, a regime observed when layer coupling is moderate and as vortices become closer in each layer. This Z-shaped tripole forms for various values of stratification and of initial distances between vortices, and is therefore a robust vortex compound in two-layer quasi-geostrophic flows.