Newspapers and their digital counterparts can be considered primary, secondary, or tertiary sources depending the type of article and reporting. They are acceptable as references in specific cases.
Newspapers are widely cited in research publications as primary sources, especially by historians and social scientists working on past events or the perception and awareness of issues by the public at a given time.
News articles are not subject to peer review, and they are generally not written by experts in an academic or even professional sense. Therefore they should only be used as secondary sources when no equivalent scholarly source is available, and when they pass tests as a trustworthy source.
They are never cited as tertiary sources (reporting on research results for example), as you would rather reference the publications they are reporting on as a source.