What type of source is a Family Bible?
Family bibles of the type you describe are published works (associated with a set of information about the source) that have been changed or annotated (associated with another set of information about the source), thus they are artifacts. Historical in nature, there is also a notion of provenance--who owned it over time--associated with these source types.
In Evidence Explained (2007), Elizabeth Shown Mills addresses "Bibles with Family Data" in her chapter three, "Archives & Artifacts."
Are they primary and highly reliable, or ... secondary? 
As with any source, the annotated pages of old family bibles contain information that is subject to error, omission and oversight. We may error, too, in our ability to fully interpret all that information or our interpretation may change over time.
We work with information in the source at the detailed level. Rather than attempt to classify one source type as superior, consult and work with a variety of information from different source materials to gain a better understanding of the information and correlate the evidence.
 Whether the family information in the bible is primary or secondary information depends on the identity of the person who made the record (and/or informant), their role in the event; timeliness of the record.