Context : Cosmic rays and magnetic fields play an important role for the formation and dynamics of gaseous halos of galaxies .

Aims : Low-frequency radio continuum observations of edge-on galaxies are ideal to study cosmic-ray electrons ( CREs ) in halos via radio synchrotron emission and to measure magnetic field strengths .
Spectral information can be used to test models of CRE propagation .
Free–free absorption by ionized gas at low frequencies allows us to investigate the properties of the warm ionized medium in the disk .

Methods : We obtained new observations of the edge-on spiral galaxy NGC 891 at 129–163 MHz with the LOw Frequency ARray ( LOFAR ) and at 13–18 GHz with the Arcminute Microkelvin Imager ( AMI ) and combine them with recent high-resolution Very Large Array ( VLA ) observations at 1–2 GHz , enabling us to study the radio continuum emission over two orders of magnitude in frequency .

Results : The spectrum of the integrated nonthermal flux density can be fitted by a power law with a spectral steepening towards higher frequencies or by a curved polynomial .
Spectral flattening at low frequencies due to free–free absorption is detected in star-forming regions of the disk .
The mean magnetic field strength in the halo is 7 \pm 2 \mu G. The scale heights of the nonthermal halo emission at 146 MHz are larger than those at 1.5 GHz everywhere , with a mean ratio of 1.7 \pm 0.3 , indicating that spectral ageing of CREs is important and that diffusive propagation dominates .
The halo scale heights at 146 MHz decrease with increasing magnetic field strengths which is a signature of dominating synchrotron losses of CREs .
On the other hand , the spectral index between 146 MHz and 1.5 GHz linearly steepens from the disk to the halo , indicating that advection rather than diffusion is the dominating CRE transport process .
This issue calls for refined modelling of CRE propagation .

Conclusions : Free–free absorption is probably important at and below about 150 MHz in the disks of edge-on galaxies .
To reliably separate the thermal and nonthermal emission components , to investigate spectral steepening due to CRE energy losses , and to measure magnetic field strengths in the disk and halo , wide frequency coverage and high spatial resolution are indispensable .