Is there anyway to merge a line Shapefile Feature Class and a polygon Shapefile Feature Class?
Input shape types are not equal
Shapefiles can store only single type of geometry (in your case either polygons or lines, not both). So, a shapefile cannot contain both lines and polygons.
Another thing is that a single feature should have a discrete geometry type. Certain geometric operations cannot be performed on multiple geometry types without converting one or both of them.
You cannot store polygons, lines or points in the same feature class. What you can do is create a feature dataset. A feature dataset is a collection of related feature classes that share a common coordinate system. Feature datasets are used to spatially or thematically integrate related feature classes. Does this help? You can maintain your lines and polygons feature classes in the feature dataset for ease of use.
You can merge Line FC's and Polygon FC's into a new Polygon FC using "Feature to Polygon". An Advanced License is required.