C# – Is it possible to set a checked listview item to mixed state

There is no real difference. SetItemCheck calls SetItemCheckedState like so:

public void SetItemChecked(int index, bool value)
{
    this.SetItemCheckState(index, value ? CheckState.Checked : CheckState.Unchecked);
}

Like you've already assumed, I guess it's just a helper-method to make things simpler for the developer.

If you would like to have an inderterminate checkbox which becomes checked on all browsers on click (or at least on IE, Chrome and FF5+), you need to initialise the checked attribute correctly, as shown here http://jsfiddle.net/K6nrT/6/. I have written the following functions to help you:

/// Gives a checkbox the inderminate state and the right
/// checked state so that it becomes checked on click
/// on click on IE, Chrome and Firefox 5+
function makeIndeterminate(checkbox)
{
    checkbox.checked = getCheckedStateForIndeterminate();
    checkbox.indeterminate = true;
}

and the interesting function which relies on feature detection:

/// Determine the checked state to give to a checkbox
/// with indeterminate state, so that it becomes checked
/// on click on IE, Chrome and Firefox 5+
function getCheckedStateForIndeterminate()
{
    // Create a unchecked checkbox with indeterminate state
    var test = document.createElement("input");
    test.type = "checkbox";
    test.checked = false;
    test.indeterminate = true;

    // Try to click the checkbox
    var body = document.body;
    body.appendChild(test); // Required to work on FF
    test.click();
    body.removeChild(test); // Required to work on FF

    // Check if the checkbox is now checked and cache the result
    if (test.checked)
    {
        getCheckedStateForIndeterminate = function () { return false; };
        return false;
    }
    else
    {
        getCheckedStateForIndeterminate = function () { return true; };
        return true;
    }
}

No image tricks, no jQuery, no extra attributes and no event handling involved. This relies only on simple JavaScript initialisation (note that the "indeterminate" attribute cannot be set in the HTML markup, so JavaScript initialisation would have been required anyway).