Though Jehu is a biblical character, this particular event is not chronicled in the Bible. An earlier mention of Israel during the reign of Shalmaneser appears on another stela, the Kurkh Monolith. Inscribed hereon is that Ahab contributed 2,000 chariots and 10,000 soldiers to an alliance of kings that was attempting to resist the conquering armies of Shalmaneser. References such as these are not contradicted by the Bible. The Bible just does not mention them.
Archaeology is an interpretive science.
However, if presented honestly and if not colored with a liberal bias, biblical archaeology never contradicts the Bible. Sometimes archaeological discoveries, though depict events that are not specifically mentioned in the Bible. Further, the Bible records characters, places and events that have not been discovered by archaeologists. Yet, whenever the Bible and archaeology address the same things, they always concur. The external evidence of biblical archaeology is a fitting companion to biblical internal evidence.