Thanks for the image.
You can try to use DAPI channel for IdentifyPrimaryObjects, name these objects "nuclei" for instance
and Green channel for IdentifySecondaryObjects, name these objects "cytoplasm" for instance.
In IdentifySecondaryObjects, try method "Distance - N" and adjust N to capture as much cytoplasm as possible. Neurons and dendrites are indeed very challenging to segment correctly.
After having identified objects (nucle, cytoplasm), you can then measure signal of interest as usual with MeasureObjectIntensity.