In this paper, we give an equivariant compactification of the space $${\mathbb {P}}{\text {Flat}}(\Sigma )$$ of homothety classes of half-translation structures on a compact, connected, orientable surface $$\Sigma $$ . We introduce the space $${\mathbb {P}}{\text {Mix}}(\Sigma )$$ of homothety classes of mixed structures on $$\Sigma $$ , that are $${\text {CAT}}(0)$$ tree-graded spaces in the sense of Drutu and Sapir, with pieces which are $${\mathbb {R}}$$ -trees and completions of surfaces endowed with half-translation structures. Endowing $${\text {Mix}}(\Sigma )$$ with the equivariant Gromov topology, and using asymptotic cone techniques, we prove that $${\mathbb {P}}{\text {Mix}}(\Sigma )$$ is an equivariant compactification of $${\mathbb {P}}{\text {Flat}}(\Sigma )$$ , thus allowing us to understand in a geometric way the degenerations of half-translation structures on $$\Sigma $$ . We finally compare our compactification to the one of Duchin–Leininger–Rafi, based on geodesic currents on $$\Sigma $$ , by the mean of the translation distances of the elements of the covering group of $$\Sigma $$ .