I occasionally answer questions on ENVI/IDL and ArcGIS/Python integration.
ENVI functions are available as "tools" through the ArcGIS GUI toolbox:
"With ENVI 4.8, ENVI’s scientifically proven image analysis capabilities will be available as discrete tools in the ArcGIS toolbox and accessible directly from ArcGIS desktop and server environments. Upon installation of ENVI products, a selection of powerful image processing and analysis tools will be available within ArcGIS."
A list of those tools is here (in the context of licensing, but just ignore that): http://www.ittvis.com/ProductsServices/ENVI/ToolsLicensing.aspx
IDL can also be accessed for extension of ENVI/IDL functionality:
"developing customized ENVI tools can be done using simple IDL scripting and wrappers that facilitate the integration of ENVI tools with the ArcGIS platform."
Here's a whitepaper: http://www.ittvis.com/portals/0/whitepapers/ENVI_Tools_ArcGIS_Server_WP_Tutorial.pdf