SQL Server 2012 :: Trying To Add Third Grouping Set To Return Average Aggregate

i'm building a query to return metrics that will drive 3 seperate pivot tables showing

1. Total count of LineItems per D_Type each month
2. Total count of LineItems per Status each month
3. Avg count of LineItems per Invoice each month

I am able to get the first two, but having hard time with the 3rd.

Here's some representative ddl
create table Remediation
(Invoice nvarchar(10), D_Type nvarchar(20), Status nvarchar(20), RemediationDate datetime);

insert into Remediation values
--this will create data for Jan, 2014
('501', 'Recycle', 'Pass', getdate()-30),
('501', 'Reuse', 'Pass', getdate()-30),
('501', 'Remarket', 'Fail', getdate()-30),

[code]....

how to add the average metric to this query?