Getting the Wrong Transfer Function for Controls Problem
Consider the parallel RL network. The admittance is
$$Y = \frac{1}{Z} = \frac{1}{s} + 0.5 \to Z = \frac{s}{0.5s + 1}$$

Now apply the voltage divider equation and multiply the numerator and denominator by 0.5s + 1
$$H = \frac{Z}{Z + 1} = \frac{s}{1.5s + 1} = \frac{2s}{3s + 2}$$

Your answer seems correct.