We prove a new non-splitting result for the cohomology of the Milnor fiber, reminiscent of the classical result proved independently by Lazzeri, Gabrielov, and Lê in 1973-74. We do this while exploring a conjecture of Bobadilla about a stronger version of our nonsplitting result. To explore this conjecture, we define a new numerical invariant for hypersurfaces with 1-dimensional critical loci: the beta invariant. The beta invariant is an invariant of the ambient topological-type of the hypersurface, is non-negative, and is algebraically calculable. Results about the beta invariant remove the topology from Bobadilla's conjecture and turn it into a purely algebraic question.2010 Mathematics Subject Classification. 32B15, 32C35, 32C18, 32B10.