Our goal is to study the evolution of the $B-$band luminosity function (LF) since $z=1$ using ALHAMBRA data. We used the photometric redshift and the $I-$band selection magnitude probability distribution functions (PDFs) of those ALHAMBRA galaxies with $Ileq24$ mag to compute the posterior LF. We statistically studied quiescent and star-forming galaxies using the template information encoded in the PDFs. The LF covariance matrix in redshift-magnitude-galaxy type space was computed, including the cosmic variance. That was estimated from the intrinsic dispersion of the LF measurements in the 48 ALHAMBRA sub-fields. The uncertainty due to the photometric redshift prior is also included in our analysis. We modelled the LF with a redshift-dependent Schechter function affected by the same selection effects than the data. The measured ALHAMBRA LF at $0.2leq z<1$ and the evolving Schechter parameters both for quiescent and star-forming galaxies agree with previous results in the literature. The estimated redshift evolution of $M_B^* propto Qz$ is $Q_{rm SF}=-1.03pm0.08$ and $Q_{rm Q}=-0.80pm0.08$, and of $log phi^* propto Pz$ is $P_{rm SF}=-0.01pm0.03$ and $P_{rm Q}=-0.41pm0.05$. The measured faint-end slopes are $alpha_{rm SF}=-1.29pm0.02$ and $alpha_{rm Q}=-0.53pm0.04$. We find a significant population of faint quiescent galaxies, modelled by a second Schechter function with slope $beta=-1.31pm0.11$. We find a factor $2.55pm0.14$ decrease in the luminosity density $j_B$ of star-forming galaxies, and a factor $1.25pm0.16$ increase in the $j_B$ of quiescent ones since $z=1$, confirming the continuous build-up of the quiescent population with cosmic time. The contribution of the faint quiescent population to $j_B$ increases from 3% at $z=1$ to 6% at $z=0$. The developed methodology will be applied to future multi-filter surveys such as J-PAS.
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