The development of continuous glucose monitoring (CGM) systems has enabled people with type 1 diabetes mellitus (T1DM) to track their glucose trajectory in real-time and inspired research in personalised glucose prediction. In this paper, our aim is to predict postprandial abnormal-glycemia events. Different from prior research which focuses on hypoglycemia only, we make the first attempt to establish our problem as the joint prediction of hyperglycemia and hypoglycemia. On this basis, we propose a machine learning model that learns from the pattern of 1 hour past glucose and makes predictions for the two tasks simultaneously using a unified backbone. Key benefits of our methodology include 1) requiring only the CGM sequence as the input, thus making it more widely applicable than other counterparts using extra inputs such as the nutrition details, and 2) minimising the computational cost as the two tasks are unified into a single model. Our experiments on the openly available OhioT1DM dataset achieve state-of-the-art performance (Matthew's correlation coefficient of 0.61 for hyperglycemia and 0.48 for hypoglycemia). To encourage further study, we release our codes at https://github.com/r-cui/PostprandialHyperHypoPrediction under the MIT license.