Automator Service: Parent of input from files or folders
The curly-brace portion of on run {input, parameters} creates a list and as such you need to address input as a list.

The following example assumes only one file or folder gets passed to the Service:

on run {input, parameters}
    tell application "System Events"
        set thePath to POSIX path of (container of (item 1 of input))
    end tell
    return thePath
end run


Can your Service receive more then one file or folder at a time? ... If yes, then you'll need to incorporate the code below.

The following example assumes multiple files or folders gets passed to the Service:

on run {input, parameters}
    set pathList to {}
    repeat with itemNum from 1 to count of input
        tell application "System Events"
            copy POSIX path of (container of (item itemNum of input)) to end of pathList
        end tell
    end repeat
    return pathList
end run




Reference: Getting the path of the parent folder of a file?