I don't think there's any special interpretation - the output of an FIR filter is the convolution of the input sequence with the filter impulse response, it doesn't really matter whether either or both are real-valued or complex-valued. If input sequence s = a + ib and filter h = c + id (a, b, c, d are real-valued sequences), then s conv h is just going to be

a conv c - b conv d + i (a conv c + b conv d)

Does that make sense?

Thanks! That explains what I am observing as the output of the filter

(a conv c + i a conv c) when the input signal is real. I have to combine the real and imaginery parts to get the actual magnitude of the input signal.

Please ALLOW me to add an additional point of view. Generally filters are easier interpreted in frequency domain since the filters are designed to have certain frequency response. The required frequency response determines the filter coefficients.The FIR filler with real coefficients have complex conjugate zeros laying on the circumference of the unity circle on the z-plane. This results in a symmetrical frequency response around the the zero normalized frequency 2 pi f/fs.

FIR Filters with complex coefficients leads to complex zeros which are not complex conjugate. Consequently, their frequency response will be unsymmetrical around the zero normalized frequency. So, they are used in filtering complex exponential signals, single sideband modulation and frequency multiplexing.

In conclusion, the complex coefficients can be better interpreted in frequency domain.

I hope i shed some light on the answer of your question.