Coughing up blood (hemoptosis) is usually not associated with CHF. More than likely, people will cough up blood if they are really coughing hard and are taking too much blood
thinner medication. Blood can also come from the lungs, but it is usually darker in color (like rust). Also, you may also be right that the blood could be coming from the nose. A nosebleed can drip down the back of someone's throat, which they then cough up, making them to think they are coughing up blood. However, you would usually also see blood coming out of the nose as well.
Since this is a new symptom, I would let your dad's health care provider know your concerns today. He should be examined if he is coughing up blood, as this can be the sign of something serious.