Background: Detailed spectroscopy of neutron-rich, heavy, deformed nuclei is of broad interest for nuclear astrophysics and nuclear structure. Nuclei in the r-process path and following freeze-out region impact the resulting r-process abundance distribution, and the structure of nuclei midshell in both proton and neutron number helps to understand the evolution of subshell gaps and large deformation in these nuclei. Purpose: We aim to improve the understanding of the nuclear structure of Gd160, specifically the Kπ=4+ bands, as well as study the β decay of Eu160 into Gd160. Methods: High-statistics decay spectroscopy of Gd160 resulting from the β-decay of Eu160 was collected using the GRIFFIN spectrometer at the TRIUMF-ISAC facility. Results: Two new excited states and ten new transitions were observed in Gd160. The β-decaying half-lives of the low- and high-spin isomers in Eu160 were determined, and the low-spin state's half-life was measured to be t1/2=26.0(8) s, ≈16% shorter than previous measurements. Lifetimes of the two Kπ=4+ bandheads in Gd160 were measured for the first time, as well as γ-γ angular correlations and mixing ratios of intense transitions out of those bandheads. Conclusions: Lifetimes and mixing ratios suggest that the hexadecapole phonon model of the Kπ=4+ bandheads in Gd160 is preferred over a simple two-state strong mixing scenario, although further theoretical calculations are needed to fully understand these states. Additionally, the 1999.0-keV state in Gd160 heavily populated in β decay is shown to have positive parity, which raises questions regarding the structure of the high-spin β-decaying state in Eu160.