  A sample of about 5500 $\bar B^0 \to D^{*+} \rho^-$ and 700 $\bar B^0 \to
D^{*+} a_1^-$ events is identified, using the technique of partial
reconstruction, among 22.7 $B\bar B$ pairs collected by the BaBar experiment at
the PEP-II storage ring. With these events, the $B^0$ lifetime is measured to
be $1.616 \pm 0.064 \pm 0.075$ ps. This measurement serves as validation for
the procedures required to measure $\sin(2\beta + \gamma)$ with partial
reconstruction of $\bar B^0 \to D^{*+} \rho^-$.
