Context. M dwarfs are prime targets for current and future planet search programs, particularly those focused on the detection and characterization of rocky planets in the habitable zone. In this context, understanding their magnetic activity is important for two main reasons: it affects our ability to detect small planets and it plays a key role in the characterization of the stellar environment. Aims: We analyze observations of the Ca ii H&K and Hα lines as diagnostics of chromospheric activity for low-activity early-type M dwarfs. Methods: We analyze the time series of spectra of 71 early-type M dwarfs collected in the framework of the HADES project for planet search purposes. The HARPS-N spectra simultaneously provide the Ca ii H&K doublet and the Hα line. We develop a reduction scheme able to correct the HARPS-N spectra for instrumental and atmospheric effects, and also to provide flux-calibrated spectra in units of flux at the stellar surface. The Ca ii H&K and Hα fluxes are then compared with each other, and their time variability is analyzed. Results: We find that the Ca ii H and K flux excesses are strongly correlated with each other, while the Hα flux excess is generally less correlated with the Ca ii H&K doublet. We also find that Hα emission does not increase monotonically with the Ca ii H&K line flux, showing some absorption before being filled in by chromospheric emission when Ca ii H&K activity increases. Analyzing the time variability of the emission fluxes, we derive a tentative estimate of the rotation period (on the order of a few tens of days) for some of the program stars, and the typical lifetime of chromospheric active regions (on the order of a few stellar rotations). Conclusions: Our results are in good agreement with similar previous studies. In particular, we find evidence that the chromospheres of early-type M dwarfs could be characterized by different filament coverage, affecting the formation mechanism of the Hα line. We also show that chromospheric structure is likely related to spectral type.