Aims: Our goal is to study the evolution of the B-band luminosity function (LF) since z 1 using ALHAMBRA data. Methods: We used the photometric redshift and the I-band selection magnitude probability distribution functions (PDFs) of those ALHAMBRA galaxies with I ≤ 24 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. Results: We modelled the LF with a redshift-dependent Schechter function affected by the same selection effects than the data. The measured ALHAMBRA LF at 0.2 ≤ 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 MB* ∝ Qz is QSF = -1.03 ± 0.08 and QQ = -0.80 ± 0.08, and of log 10φ∗ ∝ Pz is PSF = -0.01 ± 0.03 and PQ = -0.41 ± 0.05. The measured faint-end slopes are αSF = -1.29 ± 0.02 and αQ = -0.53 ± 0.04. We find a significant population of faint quiescent galaxies with MB ≳ -18, modelled by a second Schechter function with slope β = -1.31 ± 0.11. Conclusions: We present a robust methodology to compute LFs using multi-filter photometric data. The application to ALHAMBRA shows a factor 2.55 ± 0.14 decrease in the luminosity density jB of star-forming galaxies, and a factor 1.25 ± 0.16 increase in the jB 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 jB 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. Based on observations collected at the German-Spanish Astronomical Center, Calar Alto (CAHA), jointly operated by the Max-Planck-Institut für Astronomie (MPIA) at Heidelberg and the Instituto de Astrofísica de Andalucía (CSIC)