Cirrhosis with Variceal Bleeding: This is the most likely diagnosis because cirrhosis can cause jaundice due to liver dysfunction, and the presence of varices (enlarged veins) in the esophagus or stomach can lead to bleeding, resulting in haematemesis. The combination of liver disease and portal hypertension makes this a common cause of both symptoms.

Hepatic Malignancy: Liver cancer, either primary or metastatic, can cause jaundice and, if it invades or compresses nearby structures, can lead to bleeding, presenting as haematemesis.
Cholangitis: Infection of the bile ducts can cause jaundice, and if it leads to significant inflammation or erosion into nearby blood vessels, it could potentially cause bleeding.
Pancreatitis: Severe pancreatitis can cause jaundice if it affects the bile ducts and can lead to bleeding either from erosion into blood vessels or from the formation of pseudoaneurysms.

Budd-Chiari Syndrome: This condition, caused by thrombosis of the hepatic veins, can lead to acute liver failure, jaundice, and potentially bleeding due to the increased pressure and liver dysfunction. It's crucial to diagnose early because it requires specific treatment.
Vascular Malformations or Aneurysms: Rarely, vascular abnormalities in the liver or nearby structures can cause both jaundice (if they compress bile ducts) and bleeding. These conditions are critical to identify due to their high risk of severe bleeding.
Hemobilia: Bleeding into the biliary tree can cause both jaundice and gastrointestinal bleeding. It's often due to trauma, tumors, or vascular malformations and requires prompt diagnosis and treatment.

Hereditary Hemorrhagic Telangiectasia (Osler-Weber-Rendu Syndrome): A genetic disorder that leads to the formation of abnormal blood vessels, which can cause bleeding and, if they involve the liver, potentially jaundice.
Aorto-enteric Fistula: A rare condition where there's a fistula between the aorta and the gastrointestinal tract, which can cause severe bleeding. If it involves the liver or bile ducts, it could also cause jaundice.
Paroxysmal Nocturnal Hemoglobinuria (PNH): A rare, acquired, life-threatening disease of the blood characterized by the destruction of red blood cells, activation of the coagulation system, and impairment of bone marrow function. It can lead to thrombosis, including hepatic vein thrombosis, which might present with jaundice and potentially bleeding.