Is there a way to know how many bytes of a stream have been used by StreamReader?

I have a project where we need to read a file that has a text header followed by the start of the binary data. My initial attempt to read this file was something like this:

private int _dataOffset;
void ReadHeader(string path) 
{
    using (FileStream stream = File.OpenRead(path)) 
    {
        StreamReader textReader = new StreamReader(stream);

        do 
        {
            string line = textReader.ReadLine();
            handleHeaderLine(line);
        } while(line != "DATA") // Yes, they used "DATA" to mark the end of the header

        _dataOffset = stream.Position;
    }
}

private byte[] ReadDataFrame(string path, int frameNum) 
{
    using (FileStream stream = File.OpenRead(path)) 
    {
        stream.Seek(_dataOffset + frameNum * cbFrame, SeekOrigin.Begin);

        byte[] data = new byte[cbFrame];
        stream.Read(data, 0, cbFrame);

        return data;
    }
    return null;
}

The problem is that when I set _dataOffset to stream.Position, I get the position that the StreamReader has read to, not the end of the header. As soon as I thought about it this made sense, but I still need to be able to know where the end of the header is and I'm not sure if there's a way to do it and still take advantage of StreamReader.

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