Context. More gas is sometimes inferred in molecular cloud complexes than is represented in HI or CO emission, and this is called dark neutral medium (DNM). Aims. Our aim is to extend a study of DNM along 13 directions in the outskirts of Chamaeleon by determining the atomic or molecular character of the DNM along a larger sample of sightlines. Methods. We acquired ALMA ground rotational state absorption profiles of HCO + and other molecules toward 33 compact extragalactic continuum background sources seen toward the Galactic anticenter, deriving N (H 2 )= N (HCO + )/3 × 10 −9 as before. We observed J = 1−0 CO emission with the IRAM 30m telescope in directions where HCO + was newly detected. Results. HCO + absorption was detected in 28 of 3...