We use bulk magnetic susceptibility, electronic specific heat, and neutron scattering to study structural and magnetic phase transitions in Fe$_{1+y}$Se% $_x$Te$_{1-x}$. Fe$_{1.068}$Te exhibits a first order phase transition near 67 K with a tetragonal to monoclinic structural transition and simultaneously develops a collinear antiferromagnetic (AF) order responsible for the entropy change across the transition. Systematic studies of FeSe$%_{1-x}$Te$_x$ system reveal that the AF structure and lattice distortion in these materials are different from those of FeAs-based pnictides. These results call into question the conclusions of present density functional calculations, where FeSe$_{1-x}$Te$_x$ and FeAs-based pnictides are expected to have similar Fermi surfaces and therefore the same spin-density-wave AF order.