Van halven bedde literally means “from half a bed.” It is a term indicating half-siblings or half-aunts and -uncles.
For example, if somebody refers to a woman as her “zuster van halven bedde” [sister from half a bed] this refers to a half-sister and a “oom van halven bedde” [uncle from half a bed] refers to a half-uncle.
Example text: Lier, Belgium, Death certificate 216 in 1823:
… zijn verschenen Petrus Van Dessel, bakker, …, broeder van den halven bedde en … van Karel Jacob Joseph Van Dessel, …
Hence, Petrus, who comes to declare the death, is a half-brother of the deceased Karel Jacob Joseph.